There are two independent things that fiberous and foam fillings do in an enclosure. One is that they are an acoustical resistance and therefore absorb acoustic energy significantly reducing standing wave mode resonances in the box - usually at midbass frequencies for large bookshelf speakers. They also partially, and sometimes poorly, absorb all frequencies and perhaps reduce re-radiation due to reflections in the box and back out the cone, but this is not often a primary issue. Standing wave modes are powerful and cause the walls to flex more than anything else and therefore reducing standing wave energy will indirectly reduce wall flex.
These materials also act as a heat sink for the air taking it from an adiabatic system to iso-thermal. This has been extensively studied in thermodynamics simply to understand the nature of gases. The compliance of air goes up, ideally, by 1.4 when the system moves from adiabatic to iso-thermal. This is not disputed by the majority of audio professionals or thermodynamics experts but there are a few that have made absurd claims to the contrary. Here is the basic gas law theory:
http://farside.ph.utexas.edu/teaching/sm1/lectures/node53.html
Note the mention of a "heat reservoir" this is essentially a heat sink that keeps the gas at a constant temperature. The fiberous, or porous, materials have a very large surface area and they act as a thermal "mass" or heat sink keeping the gas at a constant temperature.
The compliance or effective box size ideally goes up by a factor of 1.4 with complete filling. The fundamental resonance is not linear with compliance so one should only expect resonance to go down by 1/sqrt(1.4).
Years ago I did not think that foam had enough surface area to be as effective as fiberous materials but I was wrong, it is actually quite good. All of these materials have different frequency dependent acoustic impedances making some better than others in particular applications.
Fibers moving is a second order effect and has little to do with the above concepts as I understand it.
Tom Nousaine's "Filler Up" Article in .pdf:
http://www.nousaine.com/pdfs/Box Stuffing.pdf